(a) Use the fact that the population was 250 million in 1990 ( t = 0) to formula
ID: 2849005 • Letter: #
Question
(a) Use the fact that the population was 250 million in 1990 (t = 0) to formulate a logistic model for the population of a particular region. (Assume the carrying capacity is 4500 million.)
P =
(b) Determine the value of k in your model by using the fact that the population in 2000 was 275 million. (Round your answer to eight decimal places.)
k =
(c) Use your model to predict the population in the years 2100 and 2200. (Round your answers to the nearest whole number.)
________ million people in 2100
________million people in 2200
Explanation / Answer
a) P = Po ekt
==> P = 250ekt
b) when t = 10, P = 275 (take t = 10 for year 2000 since counting starts from 1990)
==> 275 =250ek(10)
==> e10k = 275/250
==> e10k = 11/10
apply natural logarithms on both sides
==> ln e10k = ln (11/10)
==> 10k = ln (11/10)
==> k = (1/10) ln (11/10) = 0.00953102
c) P = 250e0.00953t
when t = 110
P = 250e0.00953(110) = 713.2792 = 713 million
when t= 210
P = 250e0.00953(210) = 1850.06 = 1850 million
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